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A novel voltage regulation strategy for the electric power delivery system of a 6000-m ROV
Applied Ocean Research 80 (2018) 112–117
Contents lists available at ScienceDirect
Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
A novel voltage regulation strategy for the electric power delivery system of a 6000-m ROV Qi Chena, Zhaobing Liub,c,d,
T
⁎
a
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China c Hubei Provincial Engineering Technology Research Center for Magnetic Suspension, Wuhan University of Technology, Wuhan 430070, China d Institute of Advanced Materials and Manufacturing Technology, Wuhan University of Technology, Wuhan 430070, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: ROV Voltage regulation Deep sea Piecewise linear fitting
Owing to the increasing demand for deep sea exploration, remotely operated vehicles (ROVs) that can conduct scientific tasks up to a depth of 6000 m are essential for exploring unknown areas. For electrically propelled ROVs, a voltage regulation system is used to maintain the load-side voltage within a limited range during power load variation. The load-side voltage fluctuated frequently during load variation, thus challenging the design of the voltage regulation system. Hence, we propose a novel voltage regulation strategy in the ship-side of a 6000m-deep ROV system. In this strategy, the nonlinear relationship of the compensated voltage in the ship-side and the active current in the umbilical cable are solved by piecewise linear fitting using the least-squares method. Subsequently, a feedback PID controller is designed to achieve a faster dynamic response and maintain a stable load-side voltage. The real applications of the ROV system for oceanographic surveys demonstrated that the fast response and high accuracy of the voltage regulation system for intense fluctuations of the load-side voltage could be achieved.
1. Introduction A remotely operated vehicle (ROV) is an effective platform for deepsea investigation and observation. A long electro-optic umbilical cable connecting an ROV to the master ship is used for power delivery and data exchange, enabling scientists to conduct deep-sea surveys and obtain samples in real time. A 6000-m-deep rated electrical work-class ROV has been designed by the Shenyang Institute of Automation (SIA) for oceanographic research, as shown in Fig. 1. The 6000-m ROV comprised an aluminum frame, buoyancy pack, control unit, manipulators (Schilling, USA), thrusters (Sub-Atlantic, UK), and ancillary equipment (cameras, sonars, etc.). The major specifications of the ROV are shown in Table 1. To guarantee excellent dynamics performance, the ROV is propelled by seven electro-thrusters. The electrically propelled ROVs can decrease the weight and size of the system for equipping more sophisticated tools packages to perform a variety of sea-floor surveys. The efficiency of the electrically propelled ROVs was up to 43%, much higher than the 15% efficiency of electro-hydraulic vehicles [1,2]. Therefore, most newly developed deep-sea ROVs have employed electric thrusters as their propulsion system [3], such as the ROSUB 6000 developed by the National Institute of Ocean Technology
⁎
in India [4], VICTOR 6000 developed by IFREMER in France [5], Kiel 6000 developed by the Leibniz Institute of Marine Sciences in Germany [6], and Jason 2 developed by WHOI in the USA [7]. The power delivery system of the 6000-m ROV consists of a surface power unit and a subsea power unit, as shown in Fig. 2. To reduce the voltage drop on the umbilical cable and minimize the transformer of the subsea power unit, the ship power of 380 V AC at 50 Hz is converted to 3500 V AC at 400 Hz using the surface power unit that consists of a three-phase rectifier, a sinusoidal pulse width wave modulation (SPWM) inverter, a voltage source inverter, and a step-up transformer. The three-phase rectifier converts the AC power into DC power, and the SPWM inverter based on a PID controller converts the DC power into a 400 Hz AC output. Subsequently, the AC output is stepped up to 3500 V AC by the step-up transformer. In the subsea power unit, the 3500 V AC power is converted to approximately 600 V DC power for the seven brushless DC thrusters. The normal operating voltage of the thrusters is 600 V. The maximum operating voltage is 620 V, and the minimum voltage is 550 V. Overvoltage may cause damages to the control circuit of the thrusters, and undervoltage will decrease the efficiency of the thrusters significantly. However, owing to the impedance of the umbilical cable, the voltage fluctuation on the tether cable is large for the
Corresponding author: School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China. E-mail address: [email protected] (Z. Liu).
https://doi.org/10.1016/j.apor.2018.08.020 Received 14 March 2018; Received in revised form 24 August 2018; Accepted 30 August 2018 0141-1187/ © 2018 Elsevier Ltd. All rights reserved.
Applied Ocean Research 80 (2018) 112–117
Q. Chen, Z. Liu
side voltage cannot achieve a satisfactory response for protecting the thrusters. Compared to the voltage at the subsea end, the output current of the surface power unit can be measured instantly. Thus, the feedback control of the active current in the umbilical cable could achieve a faster dynamic response. To obtain an accurate computation of the compensated voltage, the relationship between the compensated voltage and the active current is required. However, owing to the presence of nonlinear devices such as transistors, transformers, and thrusters, a precise representation of the compensated voltage is difficult to derive using a mathematical model. It would involve many approximations that could be vastly different from the actual parameter values, which are frequency dependent [14]. However, the inverted voltage contains many harmonic contents. The overvoltage in long-cable PWM drives exhibits a difference of approximately 20% between the simulation and experimental results [15]. It is therefore useful to obtain the equations of the compensated voltage from the experimental data. A piecewise linear model is a simple and effective approach for studying nonlinear systems. The key advantage of piecewise linear approximation is the translation to linear arithmetic [16]. Fortunately, the piecewise linear modeling of power transmission has been well studied. For example, piecewise matrix and the finite difference time domain method are combined to calculate the module of parallel transmission lines [17]. Piecewise approximation is applied to derive the broadband over power line transfer function [18]. It can be also applied to an AC power flow, in which the voltage and reactive power are modeled [19]. Therefore, in this work, piecewise linear fitting based on the least-squares method is first used to obtain the relationship of the compensated voltage and the active current in the umbilical cable. Subsequently, the compensated voltage can be derived according to the active current in the umbilical cable, thus maintaining the load-side voltage within a stable range. Finally, the sea trials are performed to prove the effectiveness and performance of the proposed voltage regulation system.
Fig. 1. The 6000-m ROV designed by SIA. Table 1 The specifications of the 6000-m ROV. Diving depth
6000 m
Size (L × H × W) Mass Payload Power Degree-of-freedom Speed Umbilical cable Thrusters
3.3 m × 1.8 m × 2.6 m 3000 kg (in air) Up to 100 kg 35 kW 6 2 knots Diameter Nominal Supply Voltage Max Current Max Output
2. The novel voltage regulation strategy The 50 Hz AC input voltage is converted into DC voltage by an uncontrolled rectifier. The SPWM generator is responsible for generating a series pulse width ranging wave to control the inverter circuit switching device on and off such that the DC voltage can be inverted into an AC voltage with the desired frequency and voltage. The series pulse wave is generated by comparing the sinusoidal modulating signal with a high-frequency triangular carrier signal. The output frequency is controlled by the sinusoidal modulation cycle, and the output voltage is controlled by the modulation index. The modulation index is defined as the ratio of the amplitude of the modulation signal with the amplitude of the carrier signal. Because the frequency is set to 400 Hz, only the modulation index needs to be changed to change the output voltage. To maintain the output voltage of the voltage source inverter at the desired voltage, the PID controller is designed to control the modulation index of the SPWM generator. The input value of the PID controller is the measured output voltage and the desired voltage. The desired voltage is the sum of the preset voltage and the compensated voltage. The compensated voltage can be derived by the active current in the umbilical cable. The preset voltage is defined by the ROV operator according to the preset voltage on the load-side in different operation conditions. The voltage compensator can produce a compensated voltage according to the active current in the umbilical cable, thus reducing the fluctuation voltage. The strategy block of the novel voltage regulation system is shown in Fig. 4. The major specifications of the voltage regulation system are shown in Table 2. The steep voltage on the umbilical cable is affected by the current in the cable and the impedances of the cable and load. The impedance of the cable is a combination of resistances, distributed capacitances, and winding inductances that are distributed along the umbilical cable, as shown in Fig. 5. The impedance of each section is also different, which
17.3 mm 600 V DC 10 A 100 Kgf
thrusters. Setting the output voltage of the surface power unit to 3400 V, the input voltage of the subsea power unit will drift from 3360 V at the noload condition to 2800 V at the full-power load condition. The maximum voltage dip at the end of the umbilical cable can reach up to 600 V. As shown in Fig. 3, when the load varies, the active current in the umbilical cable will change, and the 600-V circuit voltage for the thrusters will drift from nearly 700 V to 600 V, accordingly. The overvoltage in the 600-V circuit is dangerous for the control circuit of the thrusters. Maintaining the load-side voltage constant is essential to achieve a healthy condition for the thrusters [8]. The voltage regulation system can be used to maintain the load-side voltage within a stable range during power load variation. To the best of the authors’ knowledge, the voltage regulation systems for 6000-m deep ROVs equipped with 600-V thrusters have not been reported yet, which is the novelty of this work. Moreover, according to recent literature, many state-feedback controller schemes, such as the feedback linearization method [9,10], deadbeat control [11,12], and cascade control [13], have been widely employed for voltage regulation systems. Comparing the measured voltage with the reference voltage of the load-side, the voltage distortions occurred under nonlinear loads can be eliminated by the feedback controller. However, the time interval for sampling and transferring affects the dynamic performance as a time delay; therefore, the traditional controller by the feedback of the load113
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Q. Chen, Z. Liu
Fig. 2. Structure of the surface power unit and the subsea power unit. Table 2 Specifications of the voltage regulation system. Step-up transformer
280/3500, Δ→Y, 3-phase, 400 Hz
Frequency converter
Voltage accuracy Frequency accuracy (400 Hz) Response time Total Harmonic Distortion
0.5% 0.1 Hz ≤2.0 ms ≤3.0%
will lead to a heavy computation complexity. Additionally, the power transmission system exhibits a nonlinear behavior owing to the nonlinear characteristics of the transistors, step-up transformer of the voltage source inverter, step-down transformer, and thrusters of the loadside. To maintain the 600 V circuit voltage of the thrusters, the output voltage of the surface-side should be compensated according to the load variation. To determine the control function of the compensation system, a series of tests have been conducted in the tank that can reasonably simulate the real condition, as shown in Fig. 6. The current in
Fig. 3. The experimental data of the 600-V circuit voltage during load variation.
Fig. 4. Structure of the proposed novel voltage regulation strategy. 114
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Q. Chen, Z. Liu
Fig. 5. The impedance model of the umbilical cable.
umbilical cable; n is the number of points in the kth straight line; ak and bk are the polynomial coefficients. The continuity constraint is used such that the adjacent lines share the same joint point. The coefficients of Eq. (1) can be derived by the least-squares algorithm that minimizes the sum of square differences between the fitted function and the trial observations: n
∑i =1 (f (xi) − yi )2
Minimize s =
(2)
f(xi) is the value of the fitted function at xi, and yi is the compensated voltage at xi. The minimum of the function can be found by analyzing its partial derivatives: n df ds = 2 ∑ (f (x i ) − yi ) i=1 dx dx
Fig. 6. ROV being tested in the tank.
ak and bk can be derived by equating the partial derivatives to zero and solving the resulting system of equations:
the umbilical cable with different load conditions can be measured by changing the control values of the thrusters. The experiment is designed such that the compensated voltage is continuously adjusted until the 600-V circuit voltage maintains 600 V at different active currents. From the experimental data shown in Fig. 7, the compensated voltage has a nonlinear relationship with the active current in the umbilical cable. For a quick calculation of the compensated voltage, the approximation method using piecewise linear fitting is adopted. Through the piecewise linear fitting with continuous straight lines, the nonlinear function of the compensated voltage with the active current can be approximated by a set of first-order polynomials, as in Eq. (1): fk(xi)=akxi+bk (k = 1,2,…m, i = 1,2,…n)
(3)
df
n
∑i =1 (f (xi) − yi ) dx
=0
(4)
The derivation of the nodes of the straight lines is extremely important for reducing the approximation error. In general, more piecewise straight lines could yield better approximation. However, too many lines will complicate computations. Herein, an automatic piecewise linear fitting method is proposed. The nodes of the straight lines can be derived automatically. Fig. 8 depicts the strategy and the workflow of the proposed approach. First, the coefficient of the 1st straight line is computed. If the sum of square differences between the fitted function and the trial observations of the 1st line S1 is less than the limited error EL, the interval of the line will be increased. The setting value of EL should satisfy the calculated precision of the compensated voltage, depending on experience. The computed and compared process will continue until S1 exceeds the limited error EL. Subsequently, the function and linear fitting progress of the first line is completed. The computed progress will continue until all the linear fitting computations are completed.
(1)
where fk(xi) is the fitted linear function used in kth straight line; m is the number of straight lines; xi is the sampled active current in the
3. Sea trials To evaluate the effectiveness and robustness of the proposed voltage regulation strategy in real operation conditions, sea trials were performed in September 2017. Maintaining the voltage of the 600-V circuit within the preset range in a real operation condition is difficult, because the load power will change quickly and significantly when the ROV system is conducting different missions. Through piecewise linear fitting with the least-squares method, the functions of the compensated voltage are derived as f(x) = 21 Fig. 7. Compensated voltage response for maintaining 600-V circuit voltage during load variation.
0 < x < 2.1
f(x) = 61.6x−114.8 115
2.1 < x < 3.9
(5) (6)
Applied Ocean Research 80 (2018) 112–117
Q. Chen, Z. Liu
Fig. 9. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 570 V.
Fig. 8. Workflow of the proposed novel voltage compensation strategy.
f(x) = 69.1x−140
3.9 < x < 6.3
(7)
f(x) = 42.8x+47.1
6.3 < x
(8)
Fig. 10. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 580 V.
where the limited error EL is set to 2 V (the compensated voltage ranging from 21 V to 400 V; therefore, 2 V can yield a high precision up to 0.5%). At the no-load condition or the active current in the umbilical cable being less than 2.1 A, the current is primarily used to charge the capacitance of the umbilical cable. Therefore, a constant compensated voltage is adopted. At different operating conditions, the nonlinear relationship of the compensated voltage and the active current is divided into three piecewise linear functions as the active current is changed with the load variation. Through piecewise linear fitting using the least-squares method, the compensated voltage can be derived efficiently. The sum of the preset voltage and the compensated voltage is compared with the measured output voltage to produce the error signal as the input value of the PID controller. The PID controller will control the SPWM generator to yield a series pulse waves to the voltage source inverter for generating the desired voltage. The parameters of the PID controller can be obtained by the Ziegler–Nichols tuning technique. The parameters are set as follows:
Fig. 11. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 590 V.
plots on the right side are the active current in the umbilical cable. The step response is also shown in Fig. 12. When the control values of the thrusters appear suddenly, the active current increases from 2.5 A to 5 A, and acts as the step input to the voltage regulation controller. Therefore, the output voltage is regulated to maintain the 600 V. Results in terms of the maximum bias and the mean squared error (MSE) are shown in Table 3. It is clear that the voltage regulation controller can maintain the 600-V circuit voltage within a limited range. The sea trials presented demonstrated that the voltage regulation controller could provide a healthy condition for the thrusters.
a The proportional constant of PID controller (KP) = 0.1, b The integral constant of PID controller (KI) = 0.25, c The differential constant of PID controller (KD) = 0.002. The robustness of the controller under load variations is important to maintain a constant voltage. To evaluate the effectiveness of the novel voltage regulation controller, four cases of the preset thrusters’ voltage: 570 V, 580 V, 590 V, and 600 V are considered in the sea trials. The measured results are displayed in Fig. 9–12. When the active current in the umbilical cable changes rapidly, the 600-V circuit voltage can be still maintained within a limited range. In each figure, the plots on the left side are the 600-V circuit voltage for all thrusters, and the
4. Conclusions In this study, a novel voltage regulation strategy, where the output 116
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2017III047). References [1] R. Maloof, N. Forrester, C. Albrecht, A Brushless Electric Propulsion System for the Research Submersible Alvin, Woods Hole Oceanographic Institution, 1985, pp. 23–25. Technical Report. [2] L.L. Whitcomb, Underwater robotics: out of the research laboratory and into the field, Robotics and Automation, ICRA’00. IEEE International Conference 1 (2000), pp. 709–716. [3] R. Capocci, G. Dooly, E. Omerdi, et al., Inspection-class remotely operated Vehicles—a review, J. Mar. Sci. Eng. 5 (1) (2017) 13–46. [4] G.A. Ramadass, S. Ramesh, A.N. Subramanian, et al., Deep ocean mineral exploration in the Indian Ocean using remotely operated vehicle (ROSUB 6000), Underwater Technology (UT), Conference, (2015), pp. 1–8. [5] S. Chutia, N.M. Kakoty, D. Deka, A review of underwater robotics, navigation, sensing techniques and applications, AIR’17 Proceedings of the Advances in Robotics, (2017), pp. 325–333. [6] F. Abegg, P. Linke, Remotely operated vehicle “ROV KIEL 6000”, J. Large-scale Res. Facil. JLSRF 3 (2017) 1–7. [7] H.H. Sepulveda, P. Queffeulou, F. Ardhuin, Assessment of SARAL/AltiKa wave height measurements relative to buoy, Jason-2, and cryosat-2 data, Mar. Geod. 38 (1) (2015) 449–465. [8] N. Vedachalam, R. Ramesh, S. Ramesh, et al., Challenges in realizing robust systems for deep water submersible ROSUB6000, International Symposium on Underwater Technology, (2013), pp. 1–10. [9] D.E. Kim, D.C. Lee, Feedback linearization control of three-phase UPS inverter systems, IEEE Trans. Ind. Electron. 57 (3) (2010) 963–968. [10] D.C. Lee, J.I. Jang, Output voltage control of PWM inverters for stand-alone wind power generation systems using feedback linearization, IEEE IAS Annu. Meeting (2005) 1626–1631. [11] E. Kim, J. Kwon, J. Park, B. Kwon, Practical control implementation of a three-to single-phase online UPS, IEEE Trans. Ind. Electron. 55 (8) (2008) 2933–2942. [12] Z. Kai, K. Yong, X. Jian, C. Jian, Deadbeat control of PWM inverter with repetitive disturbance prediction, Proc. IEEE APEC (1999) 1026–1031. [13] L. Mihalache, Single loop DSP control method for low cost inverters, Proc. Int. Signal Process. Conf. (2003) 1078–1084. [14] A.F. Moreira, T.A. Lipo, G. Venkataramanan, et al., High frequency modeling for cable and induction motor overvoltage studies in long cable drives, Industry Applications Conference 3 (2001) 1787–1794. [15] A.F. Moreira, T.A. Lipo, G. Venkataramanan, et al., Modeling and Evaluation of dv/ dt Filters for AC Drives With High Switching Speed, (2001), pp. 1–14. [16] Y. Zhang, S. Sankaranarayanan, F. Somenzi, Piecewise linear modeling of nonlinear devices for formal verification of analog circuits, Formal Methods in ComputerAided Design (FMCAD), (2012), pp. 196–203. [17] D. Zhang, Y. Wen, J. Zhang, et al., Analysis and simulation of the crosstalk between High voltage cables and low voltage signal lines in EMU, Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications (MAPE), 2013 IEEE 5th International Symposium on. IEEE, (2013), pp. 632–636. [18] A.G. Lazaropoulos, Best piecewise monotonic data approximation in overhead and underground medium-voltage and low-voltage broadband over power lines networks: theoretical and practical transfer function determination, J. Comput. Eng. (2016). [19] P.A. Trodden, W.A. Bukhsh, A. Grothey, et al., Optimization-based islanding of power networks using piecewise linear AC power flow, IEEE Trans. Power Syst. 29 (3) (2014) 1212–1220.
Fig. 12. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 600 V. Table 3 Sea trial results.
Vs = 570 V Vs = 580 V Vs = 590 V Vs = 600 V
Max bias (V)
MSE (V)
5.8 5.6 4.7 5.4
1.84 1.83 1.82 1.83
voltage of the voltage source inverter is controlled by a PID controller and a voltage compensator, was developed to improve the power stability of a 6000-m-deep ROV. Through piecewise linear fitting using the least-squares method, a set of linear functions are derived to fit the curve of the compensated voltage with the active current. The experimental results by sea trials demonstrated that the voltage regulation controller can maintain a stable load-side voltage. Enhancing the stability of the load-side voltage is key to ensuring the safety of the 6000m-deep ROV and the success of top-level projects in the deep-sea exploration. Sea trials will be continually conducted to analyze the control performances and evaluate the effectiveness and robustness of the voltage regulation controller in the future. Acknowledgments This research is supported by the National Natural Science Foundation of China (Grant No. 51609236) and the Fundamental Research Funds for the Central Universities (WUT: 2017IVA017 and
117
Contents lists available at ScienceDirect
Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
A novel voltage regulation strategy for the electric power delivery system of a 6000-m ROV Qi Chena, Zhaobing Liub,c,d,
T
⁎
a
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China c Hubei Provincial Engineering Technology Research Center for Magnetic Suspension, Wuhan University of Technology, Wuhan 430070, China d Institute of Advanced Materials and Manufacturing Technology, Wuhan University of Technology, Wuhan 430070, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: ROV Voltage regulation Deep sea Piecewise linear fitting
Owing to the increasing demand for deep sea exploration, remotely operated vehicles (ROVs) that can conduct scientific tasks up to a depth of 6000 m are essential for exploring unknown areas. For electrically propelled ROVs, a voltage regulation system is used to maintain the load-side voltage within a limited range during power load variation. The load-side voltage fluctuated frequently during load variation, thus challenging the design of the voltage regulation system. Hence, we propose a novel voltage regulation strategy in the ship-side of a 6000m-deep ROV system. In this strategy, the nonlinear relationship of the compensated voltage in the ship-side and the active current in the umbilical cable are solved by piecewise linear fitting using the least-squares method. Subsequently, a feedback PID controller is designed to achieve a faster dynamic response and maintain a stable load-side voltage. The real applications of the ROV system for oceanographic surveys demonstrated that the fast response and high accuracy of the voltage regulation system for intense fluctuations of the load-side voltage could be achieved.
1. Introduction A remotely operated vehicle (ROV) is an effective platform for deepsea investigation and observation. A long electro-optic umbilical cable connecting an ROV to the master ship is used for power delivery and data exchange, enabling scientists to conduct deep-sea surveys and obtain samples in real time. A 6000-m-deep rated electrical work-class ROV has been designed by the Shenyang Institute of Automation (SIA) for oceanographic research, as shown in Fig. 1. The 6000-m ROV comprised an aluminum frame, buoyancy pack, control unit, manipulators (Schilling, USA), thrusters (Sub-Atlantic, UK), and ancillary equipment (cameras, sonars, etc.). The major specifications of the ROV are shown in Table 1. To guarantee excellent dynamics performance, the ROV is propelled by seven electro-thrusters. The electrically propelled ROVs can decrease the weight and size of the system for equipping more sophisticated tools packages to perform a variety of sea-floor surveys. The efficiency of the electrically propelled ROVs was up to 43%, much higher than the 15% efficiency of electro-hydraulic vehicles [1,2]. Therefore, most newly developed deep-sea ROVs have employed electric thrusters as their propulsion system [3], such as the ROSUB 6000 developed by the National Institute of Ocean Technology
⁎
in India [4], VICTOR 6000 developed by IFREMER in France [5], Kiel 6000 developed by the Leibniz Institute of Marine Sciences in Germany [6], and Jason 2 developed by WHOI in the USA [7]. The power delivery system of the 6000-m ROV consists of a surface power unit and a subsea power unit, as shown in Fig. 2. To reduce the voltage drop on the umbilical cable and minimize the transformer of the subsea power unit, the ship power of 380 V AC at 50 Hz is converted to 3500 V AC at 400 Hz using the surface power unit that consists of a three-phase rectifier, a sinusoidal pulse width wave modulation (SPWM) inverter, a voltage source inverter, and a step-up transformer. The three-phase rectifier converts the AC power into DC power, and the SPWM inverter based on a PID controller converts the DC power into a 400 Hz AC output. Subsequently, the AC output is stepped up to 3500 V AC by the step-up transformer. In the subsea power unit, the 3500 V AC power is converted to approximately 600 V DC power for the seven brushless DC thrusters. The normal operating voltage of the thrusters is 600 V. The maximum operating voltage is 620 V, and the minimum voltage is 550 V. Overvoltage may cause damages to the control circuit of the thrusters, and undervoltage will decrease the efficiency of the thrusters significantly. However, owing to the impedance of the umbilical cable, the voltage fluctuation on the tether cable is large for the
Corresponding author: School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China. E-mail address: [email protected] (Z. Liu).
https://doi.org/10.1016/j.apor.2018.08.020 Received 14 March 2018; Received in revised form 24 August 2018; Accepted 30 August 2018 0141-1187/ © 2018 Elsevier Ltd. All rights reserved.
Applied Ocean Research 80 (2018) 112–117
Q. Chen, Z. Liu
side voltage cannot achieve a satisfactory response for protecting the thrusters. Compared to the voltage at the subsea end, the output current of the surface power unit can be measured instantly. Thus, the feedback control of the active current in the umbilical cable could achieve a faster dynamic response. To obtain an accurate computation of the compensated voltage, the relationship between the compensated voltage and the active current is required. However, owing to the presence of nonlinear devices such as transistors, transformers, and thrusters, a precise representation of the compensated voltage is difficult to derive using a mathematical model. It would involve many approximations that could be vastly different from the actual parameter values, which are frequency dependent [14]. However, the inverted voltage contains many harmonic contents. The overvoltage in long-cable PWM drives exhibits a difference of approximately 20% between the simulation and experimental results [15]. It is therefore useful to obtain the equations of the compensated voltage from the experimental data. A piecewise linear model is a simple and effective approach for studying nonlinear systems. The key advantage of piecewise linear approximation is the translation to linear arithmetic [16]. Fortunately, the piecewise linear modeling of power transmission has been well studied. For example, piecewise matrix and the finite difference time domain method are combined to calculate the module of parallel transmission lines [17]. Piecewise approximation is applied to derive the broadband over power line transfer function [18]. It can be also applied to an AC power flow, in which the voltage and reactive power are modeled [19]. Therefore, in this work, piecewise linear fitting based on the least-squares method is first used to obtain the relationship of the compensated voltage and the active current in the umbilical cable. Subsequently, the compensated voltage can be derived according to the active current in the umbilical cable, thus maintaining the load-side voltage within a stable range. Finally, the sea trials are performed to prove the effectiveness and performance of the proposed voltage regulation system.
Fig. 1. The 6000-m ROV designed by SIA. Table 1 The specifications of the 6000-m ROV. Diving depth
6000 m
Size (L × H × W) Mass Payload Power Degree-of-freedom Speed Umbilical cable Thrusters
3.3 m × 1.8 m × 2.6 m 3000 kg (in air) Up to 100 kg 35 kW 6 2 knots Diameter Nominal Supply Voltage Max Current Max Output
2. The novel voltage regulation strategy The 50 Hz AC input voltage is converted into DC voltage by an uncontrolled rectifier. The SPWM generator is responsible for generating a series pulse width ranging wave to control the inverter circuit switching device on and off such that the DC voltage can be inverted into an AC voltage with the desired frequency and voltage. The series pulse wave is generated by comparing the sinusoidal modulating signal with a high-frequency triangular carrier signal. The output frequency is controlled by the sinusoidal modulation cycle, and the output voltage is controlled by the modulation index. The modulation index is defined as the ratio of the amplitude of the modulation signal with the amplitude of the carrier signal. Because the frequency is set to 400 Hz, only the modulation index needs to be changed to change the output voltage. To maintain the output voltage of the voltage source inverter at the desired voltage, the PID controller is designed to control the modulation index of the SPWM generator. The input value of the PID controller is the measured output voltage and the desired voltage. The desired voltage is the sum of the preset voltage and the compensated voltage. The compensated voltage can be derived by the active current in the umbilical cable. The preset voltage is defined by the ROV operator according to the preset voltage on the load-side in different operation conditions. The voltage compensator can produce a compensated voltage according to the active current in the umbilical cable, thus reducing the fluctuation voltage. The strategy block of the novel voltage regulation system is shown in Fig. 4. The major specifications of the voltage regulation system are shown in Table 2. The steep voltage on the umbilical cable is affected by the current in the cable and the impedances of the cable and load. The impedance of the cable is a combination of resistances, distributed capacitances, and winding inductances that are distributed along the umbilical cable, as shown in Fig. 5. The impedance of each section is also different, which
17.3 mm 600 V DC 10 A 100 Kgf
thrusters. Setting the output voltage of the surface power unit to 3400 V, the input voltage of the subsea power unit will drift from 3360 V at the noload condition to 2800 V at the full-power load condition. The maximum voltage dip at the end of the umbilical cable can reach up to 600 V. As shown in Fig. 3, when the load varies, the active current in the umbilical cable will change, and the 600-V circuit voltage for the thrusters will drift from nearly 700 V to 600 V, accordingly. The overvoltage in the 600-V circuit is dangerous for the control circuit of the thrusters. Maintaining the load-side voltage constant is essential to achieve a healthy condition for the thrusters [8]. The voltage regulation system can be used to maintain the load-side voltage within a stable range during power load variation. To the best of the authors’ knowledge, the voltage regulation systems for 6000-m deep ROVs equipped with 600-V thrusters have not been reported yet, which is the novelty of this work. Moreover, according to recent literature, many state-feedback controller schemes, such as the feedback linearization method [9,10], deadbeat control [11,12], and cascade control [13], have been widely employed for voltage regulation systems. Comparing the measured voltage with the reference voltage of the load-side, the voltage distortions occurred under nonlinear loads can be eliminated by the feedback controller. However, the time interval for sampling and transferring affects the dynamic performance as a time delay; therefore, the traditional controller by the feedback of the load113
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Q. Chen, Z. Liu
Fig. 2. Structure of the surface power unit and the subsea power unit. Table 2 Specifications of the voltage regulation system. Step-up transformer
280/3500, Δ→Y, 3-phase, 400 Hz
Frequency converter
Voltage accuracy Frequency accuracy (400 Hz) Response time Total Harmonic Distortion
0.5% 0.1 Hz ≤2.0 ms ≤3.0%
will lead to a heavy computation complexity. Additionally, the power transmission system exhibits a nonlinear behavior owing to the nonlinear characteristics of the transistors, step-up transformer of the voltage source inverter, step-down transformer, and thrusters of the loadside. To maintain the 600 V circuit voltage of the thrusters, the output voltage of the surface-side should be compensated according to the load variation. To determine the control function of the compensation system, a series of tests have been conducted in the tank that can reasonably simulate the real condition, as shown in Fig. 6. The current in
Fig. 3. The experimental data of the 600-V circuit voltage during load variation.
Fig. 4. Structure of the proposed novel voltage regulation strategy. 114
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Fig. 5. The impedance model of the umbilical cable.
umbilical cable; n is the number of points in the kth straight line; ak and bk are the polynomial coefficients. The continuity constraint is used such that the adjacent lines share the same joint point. The coefficients of Eq. (1) can be derived by the least-squares algorithm that minimizes the sum of square differences between the fitted function and the trial observations: n
∑i =1 (f (xi) − yi )2
Minimize s =
(2)
f(xi) is the value of the fitted function at xi, and yi is the compensated voltage at xi. The minimum of the function can be found by analyzing its partial derivatives: n df ds = 2 ∑ (f (x i ) − yi ) i=1 dx dx
Fig. 6. ROV being tested in the tank.
ak and bk can be derived by equating the partial derivatives to zero and solving the resulting system of equations:
the umbilical cable with different load conditions can be measured by changing the control values of the thrusters. The experiment is designed such that the compensated voltage is continuously adjusted until the 600-V circuit voltage maintains 600 V at different active currents. From the experimental data shown in Fig. 7, the compensated voltage has a nonlinear relationship with the active current in the umbilical cable. For a quick calculation of the compensated voltage, the approximation method using piecewise linear fitting is adopted. Through the piecewise linear fitting with continuous straight lines, the nonlinear function of the compensated voltage with the active current can be approximated by a set of first-order polynomials, as in Eq. (1): fk(xi)=akxi+bk (k = 1,2,…m, i = 1,2,…n)
(3)
df
n
∑i =1 (f (xi) − yi ) dx
=0
(4)
The derivation of the nodes of the straight lines is extremely important for reducing the approximation error. In general, more piecewise straight lines could yield better approximation. However, too many lines will complicate computations. Herein, an automatic piecewise linear fitting method is proposed. The nodes of the straight lines can be derived automatically. Fig. 8 depicts the strategy and the workflow of the proposed approach. First, the coefficient of the 1st straight line is computed. If the sum of square differences between the fitted function and the trial observations of the 1st line S1 is less than the limited error EL, the interval of the line will be increased. The setting value of EL should satisfy the calculated precision of the compensated voltage, depending on experience. The computed and compared process will continue until S1 exceeds the limited error EL. Subsequently, the function and linear fitting progress of the first line is completed. The computed progress will continue until all the linear fitting computations are completed.
(1)
where fk(xi) is the fitted linear function used in kth straight line; m is the number of straight lines; xi is the sampled active current in the
3. Sea trials To evaluate the effectiveness and robustness of the proposed voltage regulation strategy in real operation conditions, sea trials were performed in September 2017. Maintaining the voltage of the 600-V circuit within the preset range in a real operation condition is difficult, because the load power will change quickly and significantly when the ROV system is conducting different missions. Through piecewise linear fitting with the least-squares method, the functions of the compensated voltage are derived as f(x) = 21 Fig. 7. Compensated voltage response for maintaining 600-V circuit voltage during load variation.
0 < x < 2.1
f(x) = 61.6x−114.8 115
2.1 < x < 3.9
(5) (6)
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Fig. 9. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 570 V.
Fig. 8. Workflow of the proposed novel voltage compensation strategy.
f(x) = 69.1x−140
3.9 < x < 6.3
(7)
f(x) = 42.8x+47.1
6.3 < x
(8)
Fig. 10. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 580 V.
where the limited error EL is set to 2 V (the compensated voltage ranging from 21 V to 400 V; therefore, 2 V can yield a high precision up to 0.5%). At the no-load condition or the active current in the umbilical cable being less than 2.1 A, the current is primarily used to charge the capacitance of the umbilical cable. Therefore, a constant compensated voltage is adopted. At different operating conditions, the nonlinear relationship of the compensated voltage and the active current is divided into three piecewise linear functions as the active current is changed with the load variation. Through piecewise linear fitting using the least-squares method, the compensated voltage can be derived efficiently. The sum of the preset voltage and the compensated voltage is compared with the measured output voltage to produce the error signal as the input value of the PID controller. The PID controller will control the SPWM generator to yield a series pulse waves to the voltage source inverter for generating the desired voltage. The parameters of the PID controller can be obtained by the Ziegler–Nichols tuning technique. The parameters are set as follows:
Fig. 11. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 590 V.
plots on the right side are the active current in the umbilical cable. The step response is also shown in Fig. 12. When the control values of the thrusters appear suddenly, the active current increases from 2.5 A to 5 A, and acts as the step input to the voltage regulation controller. Therefore, the output voltage is regulated to maintain the 600 V. Results in terms of the maximum bias and the mean squared error (MSE) are shown in Table 3. It is clear that the voltage regulation controller can maintain the 600-V circuit voltage within a limited range. The sea trials presented demonstrated that the voltage regulation controller could provide a healthy condition for the thrusters.
a The proportional constant of PID controller (KP) = 0.1, b The integral constant of PID controller (KI) = 0.25, c The differential constant of PID controller (KD) = 0.002. The robustness of the controller under load variations is important to maintain a constant voltage. To evaluate the effectiveness of the novel voltage regulation controller, four cases of the preset thrusters’ voltage: 570 V, 580 V, 590 V, and 600 V are considered in the sea trials. The measured results are displayed in Fig. 9–12. When the active current in the umbilical cable changes rapidly, the 600-V circuit voltage can be still maintained within a limited range. In each figure, the plots on the left side are the 600-V circuit voltage for all thrusters, and the
4. Conclusions In this study, a novel voltage regulation strategy, where the output 116
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2017III047). References [1] R. Maloof, N. Forrester, C. Albrecht, A Brushless Electric Propulsion System for the Research Submersible Alvin, Woods Hole Oceanographic Institution, 1985, pp. 23–25. Technical Report. [2] L.L. Whitcomb, Underwater robotics: out of the research laboratory and into the field, Robotics and Automation, ICRA’00. IEEE International Conference 1 (2000), pp. 709–716. [3] R. Capocci, G. Dooly, E. Omerdi, et al., Inspection-class remotely operated Vehicles—a review, J. Mar. Sci. Eng. 5 (1) (2017) 13–46. [4] G.A. Ramadass, S. Ramesh, A.N. Subramanian, et al., Deep ocean mineral exploration in the Indian Ocean using remotely operated vehicle (ROSUB 6000), Underwater Technology (UT), Conference, (2015), pp. 1–8. [5] S. Chutia, N.M. Kakoty, D. Deka, A review of underwater robotics, navigation, sensing techniques and applications, AIR’17 Proceedings of the Advances in Robotics, (2017), pp. 325–333. [6] F. Abegg, P. Linke, Remotely operated vehicle “ROV KIEL 6000”, J. Large-scale Res. Facil. JLSRF 3 (2017) 1–7. [7] H.H. Sepulveda, P. Queffeulou, F. Ardhuin, Assessment of SARAL/AltiKa wave height measurements relative to buoy, Jason-2, and cryosat-2 data, Mar. Geod. 38 (1) (2015) 449–465. [8] N. Vedachalam, R. Ramesh, S. Ramesh, et al., Challenges in realizing robust systems for deep water submersible ROSUB6000, International Symposium on Underwater Technology, (2013), pp. 1–10. [9] D.E. Kim, D.C. Lee, Feedback linearization control of three-phase UPS inverter systems, IEEE Trans. Ind. Electron. 57 (3) (2010) 963–968. [10] D.C. Lee, J.I. Jang, Output voltage control of PWM inverters for stand-alone wind power generation systems using feedback linearization, IEEE IAS Annu. Meeting (2005) 1626–1631. [11] E. Kim, J. Kwon, J. Park, B. Kwon, Practical control implementation of a three-to single-phase online UPS, IEEE Trans. Ind. Electron. 55 (8) (2008) 2933–2942. [12] Z. Kai, K. Yong, X. Jian, C. Jian, Deadbeat control of PWM inverter with repetitive disturbance prediction, Proc. IEEE APEC (1999) 1026–1031. [13] L. Mihalache, Single loop DSP control method for low cost inverters, Proc. Int. Signal Process. Conf. (2003) 1078–1084. [14] A.F. Moreira, T.A. Lipo, G. Venkataramanan, et al., High frequency modeling for cable and induction motor overvoltage studies in long cable drives, Industry Applications Conference 3 (2001) 1787–1794. [15] A.F. Moreira, T.A. Lipo, G. Venkataramanan, et al., Modeling and Evaluation of dv/ dt Filters for AC Drives With High Switching Speed, (2001), pp. 1–14. [16] Y. Zhang, S. Sankaranarayanan, F. Somenzi, Piecewise linear modeling of nonlinear devices for formal verification of analog circuits, Formal Methods in ComputerAided Design (FMCAD), (2012), pp. 196–203. [17] D. Zhang, Y. Wen, J. Zhang, et al., Analysis and simulation of the crosstalk between High voltage cables and low voltage signal lines in EMU, Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications (MAPE), 2013 IEEE 5th International Symposium on. IEEE, (2013), pp. 632–636. [18] A.G. Lazaropoulos, Best piecewise monotonic data approximation in overhead and underground medium-voltage and low-voltage broadband over power lines networks: theoretical and practical transfer function determination, J. Comput. Eng. (2016). [19] P.A. Trodden, W.A. Bukhsh, A. Grothey, et al., Optimization-based islanding of power networks using piecewise linear AC power flow, IEEE Trans. Power Syst. 29 (3) (2014) 1212–1220.
Fig. 12. 600-V circuit voltage and active current in the umbilical cable when the thrusters’ voltage is set to 600 V. Table 3 Sea trial results.
Vs = 570 V Vs = 580 V Vs = 590 V Vs = 600 V
Max bias (V)
MSE (V)
5.8 5.6 4.7 5.4
1.84 1.83 1.82 1.83
voltage of the voltage source inverter is controlled by a PID controller and a voltage compensator, was developed to improve the power stability of a 6000-m-deep ROV. Through piecewise linear fitting using the least-squares method, a set of linear functions are derived to fit the curve of the compensated voltage with the active current. The experimental results by sea trials demonstrated that the voltage regulation controller can maintain a stable load-side voltage. Enhancing the stability of the load-side voltage is key to ensuring the safety of the 6000m-deep ROV and the success of top-level projects in the deep-sea exploration. Sea trials will be continually conducted to analyze the control performances and evaluate the effectiveness and robustness of the voltage regulation controller in the future. Acknowledgments This research is supported by the National Natural Science Foundation of China (Grant No. 51609236) and the Fundamental Research Funds for the Central Universities (WUT: 2017IVA017 and
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